Lightning payments offer pretty strong privacy if used correctly. Custodial wallets give you privacy from the general public, but not from the custodial provider. If you are going to use a custodial LN wallet you might as well use ecash. You can still be rugged, but at least you have privacy from both the public and the custodian.

If you care about easy to use non-custodial privacy, with the security a blockchain provides, Monero is better. If not, use ecash.